I certainly would not rule out number 5 ;) As for 3, the arguments seem to apply to any universe in which you can carry out a reproducible experiment. However, in a “classical universe” everything is, in principle, exactly knowable, and so you just don’t need a probabilistic description.
Unless there is limited information, in which case you use statistical mechanics. With perfect information you know which microstate the system is in, the evolution is deterministic, there is no entropy (macrostate concept), hence no second law, etc. Only when you have imperfect information—an ensemble of possible microstates, a macrostate—mechanics “becomes” statistical.
Using probabilistic logic in a situation where classical logic applies is either overkill or underconfidence.
In case it’s less than perfectly clear, I am very much not ruling out number 5; that’s why it’s there. But for obvious reasons there’s not much I can say about how it might be true and what the consequences would be.
Even in a classical universe your knowledge is always going to be incomplete in practice. (Perfectly precise measurement is not in general possible. Your brain has fewer possible states than the whole universe. Etc.) So probabilistic reasoning, or something very like it, is inescapable even classically. Regardless, though, it would be pretty surprising to me if mere “underconfidence” (supposing it to be so) required a quantum [EDITED TO ADD: model of the] universe.
I’m not sure if we can say much about a classical universe “in practice” because in practice we do not live in a classical universe. I imagine you could have perfect information if you looked at some simple classical universe from the outside.
For classical universes with complete information you have Newtonian dynamics. For classical universes with incomplete information about the state you can still use Newtonian dynamics but represent the state of the system with a probability distribution. This ultimately leads to (classical) statistical mechanics. For universes with incomplete information about the state and about its evolution (“category 3a” in the paper) you get quantum theory.
[Important caveat about classical statistical mechanics: it turns out to be a problem to formulate it without assuming some sort of granularity of phase space, which quantum theory provides. So it’s all pretty intertwined.]
I certainly would not rule out number 5 ;) As for 3, the arguments seem to apply to any universe in which you can carry out a reproducible experiment. However, in a “classical universe” everything is, in principle, exactly knowable, and so you just don’t need a probabilistic description.
Unless there is limited information, in which case you use statistical mechanics. With perfect information you know which microstate the system is in, the evolution is deterministic, there is no entropy (macrostate concept), hence no second law, etc. Only when you have imperfect information—an ensemble of possible microstates, a macrostate—mechanics “becomes” statistical.
Using probabilistic logic in a situation where classical logic applies is either overkill or underconfidence.
In case it’s less than perfectly clear, I am very much not ruling out number 5; that’s why it’s there. But for obvious reasons there’s not much I can say about how it might be true and what the consequences would be.
Even in a classical universe your knowledge is always going to be incomplete in practice. (Perfectly precise measurement is not in general possible. Your brain has fewer possible states than the whole universe. Etc.) So probabilistic reasoning, or something very like it, is inescapable even classically. Regardless, though, it would be pretty surprising to me if mere “underconfidence” (supposing it to be so) required a quantum [EDITED TO ADD: model of the] universe.
I’m not sure if we can say much about a classical universe “in practice” because in practice we do not live in a classical universe. I imagine you could have perfect information if you looked at some simple classical universe from the outside.
For classical universes with complete information you have Newtonian dynamics. For classical universes with incomplete information about the state you can still use Newtonian dynamics but represent the state of the system with a probability distribution. This ultimately leads to (classical) statistical mechanics. For universes with incomplete information about the state and about its evolution (“category 3a” in the paper) you get quantum theory.
[Important caveat about classical statistical mechanics: it turns out to be a problem to formulate it without assuming some sort of granularity of phase space, which quantum theory provides. So it’s all pretty intertwined.]